Question

Помогите плиз решить номер 41 и 42

Answer 1

41) 

$dispaystyle frac{100^5}{(80+20)^{10}}*50^5= frac{100^5}{100^{10}}*50^5= frac{1}{100^5}*50^5= frac{50^5}{(2*50)^5}= frac{1}{2^5}= frac{1}{32}$

42)

$dispaystyle frac{2}{1+ frac{1}{1+2^{-1}}}- frac{2}{1+ frac{1}{1-2^{-1}}}= frac{2}{1+ frac{1}{1+ frac{1}{2}}}- frac{2}{1+ frac{1}{1- frac{1}{2}}}=\\= frac{2}{1+ frac{1}{ frac{3}{2}}}- frac{2}{1+ frac{1}{ frac{1}{2}}}= frac{2}{1+ frac{2}{3}}- frac{2}{1+2}=\\= frac{2}{ frac{5}{3}}- frac{2}{3}= frac{6}{5}- frac{2}{3}= frac{18-10}{15}= frac{8}{15}$